Average Error: 9.8 → 0.1
Time: 2.9s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(1 \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(1 \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)
double f(double x, double y, double z, double t) {
        double r802312 = x;
        double r802313 = y;
        double r802314 = r802312 / r802313;
        double r802315 = 2.0;
        double r802316 = z;
        double r802317 = r802316 * r802315;
        double r802318 = 1.0;
        double r802319 = t;
        double r802320 = r802318 - r802319;
        double r802321 = r802317 * r802320;
        double r802322 = r802315 + r802321;
        double r802323 = r802319 * r802316;
        double r802324 = r802322 / r802323;
        double r802325 = r802314 + r802324;
        return r802325;
}
↓
double f(double x, double y, double z, double t) {
        double r802326 = x;
        double r802327 = y;
        double r802328 = r802326 / r802327;
        double r802329 = 1.0;
        double r802330 = 2.0;
        double r802331 = z;
        double r802332 = r802330 / r802331;
        double r802333 = r802332 + r802330;
        double r802334 = t;
        double r802335 = r802333 / r802334;
        double r802336 = r802329 * r802335;
        double r802337 = r802336 - r802330;
        double r802338 = r802328 + r802337;
        return r802338;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.8
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.8

    \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) - 2\right)}\]

  3. Simplified0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.1

    \[\leadsto \frac{x}{y} + \left(\frac{1}{\color{blue}{1 \cdot t}} \cdot \left(\frac{2}{z} + 2\right) - 2\right)\]

  6. Applied *-un-lft-identity0.1

    \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{1 \cdot 1}}{1 \cdot t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)\]

  7. Applied times-frac0.1

    \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(\frac{1}{1} \cdot \frac{1}{t}\right)} \cdot \left(\frac{2}{z} + 2\right) - 2\right)\]

  8. Applied associate-*l*0.1

    \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{1}{1} \cdot \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right)\right)} - 2\right)\]

  9. Simplified0.1

    \[\leadsto \frac{x}{y} + \left(\frac{1}{1} \cdot \color{blue}{\frac{\frac{2}{z} + 2}{t}} - 2\right)\]

  10. Final simplification0.1

    \[\leadsto \frac{x}{y} + \left(1 \cdot \frac{\frac{2}{z} + 2}{t} - 2\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y)))

  (+ (/ x y) (/ (+ 2 (* (* z 2) (- 1 t))) (* t z))))